In the description of the background of the present invention that follows reference is made to certain structures and methods, however, such references should not necessarily be construed as an admission that these structures and methods qualify as prior art under the applicable statutory provisions. Applicants reserve the right to demonstrate that any of the referenced subject matter does not constitute prior art with regard to present embodiments.
It is common in the semiconductor industry to utilize compact resistive heating element assemblies to heat a material to a desired temperature. An example of such an application is the heating of a hydrogen and oxygen gas stream in order to produce a high-purity steam.
These heating element assemblies are usually quite small in size and are designed to run from standard 120V AC nominal voltage. The combination of the physical size limitations and high voltage lead to the selection of relatively small wire diameters for the resistance heater. The use of small wire diameters can in turn lead to more frequent failures of the elements than is desirable.
In many cases, the above-described heating element assemblies can consist of two half-sections wired in series to obtain the desired electrical characteristics. If the heating elements were wired in parallel, for example, the resistance would be relatively low; and more power would be required to heat the elements to proper temperatures. One consequence of this typical in-series connection is that when one half of the element fails, the entire unit is disabled. The failure of the entire heating element assembly during a process run can generate a potentially unsafe condition and can lead to the workpieces of the process run in the furnace at that time being scrapped or requiring reworking. Scrapped lots and rework have obvious detrimental efficiency and economic implications.
In light of the above, it would be advantageous to change the connection of the two halves to a parallel configuration, so as to avoid the total failure from the failure of a single heating element. However, changing from a series connection to a parallel wiring configuration normally involves changing the heating element wire to a smaller gauge so that the parallel connection retains the same electrical characteristics as the series connection, which is necessary in order to be able to use the same power supply controls.
This problem can be described by reference to the following expressions and calculations.
Assuming a series and parallel connection of a two-section heating element assembly, the total resistance for the series connection is:Rs=R1+R2where Rs is the total resistance of the series connection, R1 is the resistance of the first section, and R2 is the resistance of the second section. The total resistance of the arrangement wired in parallel is:1/Rp=1/R1+1/R2where Rp is the total resistance of the parallel connection. Assuming that the resistance of the first and second sections are the same (R1=R2), the above expressions can be simplified as follows:Rs=2R1/Rp=2/RRp=R/2
Thus, in order to render the resistance of the series and parallel connections equal:Rs=Rp2R(s)=R(p)/2Rp=4×Rs
Thus, in the above example, the resistance must be increased by four-fold in order to switch from a series configuration to a parallel configuration.
According to the following expression it is known that resistance is inversely proportional to the gauge of a round wire:R=ρL/A=ρL/Πr2where ρ is the resistivity constant, L is the length of the wire, A is the cross-sectional area of the wire, and r is the radius of the wire. Thus a decrease in the cross-sectional area of the wire will result in the desired increase in resistance.
However, as mentioned above, resorting to smaller diameter heating element wires can greatly reduce the life and reliability of the element assembly.
Therefore, it would be desirable to provide a mechanism to permit the parallel connection of a plurality of resistive elements without resorting to reduction in the gauge of the wires.